Policy_and_Value_Iteration.ipynb

{
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  "metadata": {
    "colab": {
      "name": "Policy and Value Iteration.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/hayatrajani/reinforcement-learning/blob/main/Policy_and_Value_Iteration.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iUUXSgXJhhax"
      },
      "source": [
        "# Import required Modules"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BdblfD3eoFIr"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.patches import Rectangle\n",
        "\n",
        "%matplotlib inline\n",
        "np.set_printoptions(linewidth=np.inf)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IF3KQO08ho4Z"
      },
      "source": [
        "# Design the Grid World\n",
        "\n",
        "![Grid World](https://drive.google.com/uc?id=1vFtvKmOCfYnLVTMyQGJD3cNk0AkItm0-)\n",
        "\n",
        "The agent may start in any cell.\n",
        "\n",
        "When it reaches cell $G$, it will receive $100$ points and the episode ends.\n",
        "\n",
        "When it reaches a cell marked $*$, it will receive $10$ points and the episode continues.\n",
        "\n",
        "When it attempts to enter a cell marked $X$, it will receive $-20$ points and stay in the cell it came\n",
        "from.\n",
        "\n",
        "When it attempts to leave the grid, it will receive $-30$ points and stay where it is.\n",
        "\n",
        "All actions entering an unmarked cell will receive $-1$ point."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7bW9Hi4oQCdC"
      },
      "source": [
        "gridSize = (9,9)\n",
        "\n",
        "offGridReward = -30\n",
        "obstacleReward = -20\n",
        "starReward = 10\n",
        "goalReward = 100\n",
        "\n",
        "rewards = np.zeros(gridSize)-1\n",
        "\n",
        "obstacles = (\n",
        "    (1,5), (1,7),\n",
        "    (2,1), (2,2), (2,3), (2,4), (2,5), (2,7),\n",
        "    (3,1), (3,6),\n",
        "    (4,3), (4,4), (4,5), \n",
        "    (5,7),\n",
        "    (6,1), (6,2), (6,3), (6,4), (6,5), (6,6),\n",
        "    (7,8),\n",
        "    (8,4), (8,8)\n",
        ")\n",
        "for cell in obstacles:\n",
        "    rewards[cell] = obstacleReward\n",
        "\n",
        "stars = (\n",
        "    (0,0), (0,1), (0,2), (0,7), (0,8),\n",
        "    (1,8),\n",
        "    (3,2), (3,3), (3,4), (3,5),\n",
        "    (4,2),\n",
        "    (7,1), (7,2), (7,3), (7,4), (7,5), (7,6),\n",
        "    (8,1), (8,2), (8,3), (8,5), (8,6)\n",
        ")\n",
        "for cell in stars:\n",
        "    rewards[cell] = starReward\n",
        "\n",
        "goal = ((3,8),)\n",
        "for cell in goal:\n",
        "    rewards[cell] = goalReward\n",
        "        \n",
        "\n",
        "# define the actions N, S, E, W, NE, NW, SE, SW - indexed sequentially\n",
        "# action E (move right) indexed at 2\n",
        "allActions = ((-1,0), (1,0), (0,1), (0,-1), (-1,1), (-1,-1), (1,1), (1,-1))\n",
        "\n",
        "\n",
        "def initPolicy(actions):\n",
        "    # Choose a random action with probability 0.5 and otherwise move right\n",
        "    nActions = len(actions)\n",
        "    action_prob = np.zeros((*gridSize, nActions))   # shape: H x W x Actions\n",
        "    for action in actions:\n",
        "        action_prob[:,:,action] += 0.5+(0.5/nActions) if action == 2 else 0.5/nActions\n",
        "    for s in np.ndindex(gridSize):\n",
        "        if rewards[s] in (obstacleReward,goalReward):\n",
        "            action_prob[s] = 0\n",
        "    return action_prob\n",
        "\n",
        "\n",
        "def step(state, action, deterministic=True):\n",
        "    # all actions take place with probability 1\n",
        "    if deterministic:\n",
        "        nextState = (state[0] + action[0], state[1] + action[1])    \n",
        "        # Check if agent is within the grid\n",
        "        if 0 <= nextState[0] < gridSize[0] and 0 <= nextState[1] < gridSize[1]:\n",
        "            reward = rewards[nextState]\n",
        "            # if the agent attempts to enter cell marked X, -20 points and\n",
        "            # it stays in the same cell it came from\n",
        "            if reward == obstacleReward:\n",
        "                return [(state, 1, reward)]\n",
        "            else:\n",
        "                return [(nextState, 1, reward)]\n",
        "        # Penalty if the agent leaves the grid\n",
        "        else:\n",
        "            return [(state, 1, offGridReward)]\n",
        "    # desired action only takes place with probability 0.8\n",
        "    # with probability 0.1, agent deviates 45 deg left, or\n",
        "    # with probability 0.1, 45 deg right of desired action\n",
        "    else:\n",
        "        returns = []\n",
        "        for thetaDev, trans_prob in ((0,0.8), (-np.pi/4,0.1), (np.pi/4,0.1)):\n",
        "            rotMat = np.array([[np.cos(thetaDev),-np.sin(thetaDev)],\n",
        "                               [np.sin(thetaDev),np.cos(thetaDev)]])\n",
        "            action = np.round(rotMat @ action).astype(int)\n",
        "            nextState, _, reward = step(state, action, deterministic=True)[0]\n",
        "            returns.append((nextState, trans_prob, reward))\n",
        "        return returns\n",
        "\n",
        "\n",
        "def policyEvaluation(policy, actions, V = np.zeros(gridSize), gamma=0.9, theta=1e-4, deterministic=True):\n",
        "    # repeat\n",
        "    while True:\n",
        "        delta = 0\n",
        "        # for each state s\n",
        "        for s in np.ndindex(gridSize):\n",
        "            # if not terminal state (cells marked with G or X) i.e.\n",
        "            # a state in which the agent can perform a valid action\n",
        "            if rewards[s] not in (obstacleReward,goalReward):\n",
        "                # update the state value via a full width one step look ahead backup\n",
        "                v = 0\n",
        "                action_prob = policy[s]\n",
        "                # for each possible action from state s\n",
        "                for a in actions:\n",
        "                    # for each possible successor state resulting from action a\n",
        "                    for s_, trans_prob, reward in step(s, allActions[a], deterministic):\n",
        "                        # sum up the immediate rewards and discounted successor state values\n",
        "                        # weighted by the respective transition and action probabilities\n",
        "                        v += action_prob[a]*trans_prob*(reward + gamma*V[s_])\n",
        "                # get the maximum difference in state values\n",
        "                delta = max(delta, abs(V[s]-v))\n",
        "                V[s] = v\n",
        "        # until maximum change in state values goes below threshold\n",
        "        if delta < theta:\n",
        "            break\n",
        "    return V\n",
        "\n",
        "\n",
        "def lookahead(state, actions, V, gamma=0.9, deterministic=True):    \n",
        "    Q = np.zeros(len(actions))\n",
        "    # for each possible action from state s\n",
        "    for a in actions:\n",
        "        # for each possible successor state resulting from action a\n",
        "        for s_, trans_prob, reward in step(state, allActions[a], deterministic):\n",
        "            # estimate the expected value\n",
        "            Q[a] += trans_prob*(reward + gamma*V[s_])\n",
        "    return Q\n",
        "\n",
        "\n",
        "def policyIteration(actions, gamma=0.9, deterministic=True):\n",
        "    policy = initPolicy(actions)\n",
        "    V = np.zeros(gridSize)\n",
        "    # repeat\n",
        "    while True:\n",
        "        # policy evaluation\n",
        "        V = policyEvaluation(policy, actions, V=V)\n",
        "        # policy improvement\n",
        "        policy_stable = True\n",
        "        # for each state s\n",
        "        for s in np.ndindex(gridSize):\n",
        "            # if not terminal state (cells marked with G or X) i.e.\n",
        "            # a state in which the agent can perform a valid action\n",
        "            if rewards[s] not in (obstacleReward,goalReward):\n",
        "                # get the best action(s) as per current policy\n",
        "                aOld = np.where(policy[s]==policy[s].max())[0]\n",
        "                # estimate action values for all possible actions from state s\n",
        "                Q = lookahead(s, actions, V, gamma, deterministic)\n",
        "                # get the new best action(s)\n",
        "                aNew = np.where(Q==Q.max())[0]\n",
        "                # greedily update the policy\n",
        "                if (not np.array_equal(aOld, aNew)):\n",
        "                    policy_stable = False\n",
        "                for a in actions:\n",
        "                    policy[s][a] = 1/len(aNew) if a in aNew else 0\n",
        "        # until policy converges\n",
        "        if policy_stable:\n",
        "            return V, policy\n",
        "\n",
        "\n",
        "def valueIteration(actions, gamma=0.9, theta=1e-4, deterministic=True):\n",
        "    V = np.zeros(gridSize)\n",
        "    # repeat\n",
        "    while True:\n",
        "        delta = 0\n",
        "        # for each state s\n",
        "        for s in np.ndindex(gridSize):\n",
        "            # if not terminal state (cells marked with G or X) i.e.\n",
        "            # a state in which the agent can perform a valid action\n",
        "            if rewards[s] not in (obstacleReward,goalReward):\n",
        "                # estimate action values for all possible actions from state s\n",
        "                Q = lookahead(s, actions, V, gamma, deterministic)\n",
        "                # max over the estimated action values\n",
        "                v = np.max(Q)\n",
        "                # get the maximum difference in state values\n",
        "                delta = max(delta, abs(V[s]-v))\n",
        "                V[s] = v\n",
        "        # until maximum change in state value goes below threshold\n",
        "        if delta < theta:\n",
        "            break\n",
        "    policy = np.zeros((*gridSize, len(actions)))\n",
        "    # policy update\n",
        "    for s in np.ndindex(gridSize):\n",
        "        # if not terminal state (cells marked with G or X) i.e.\n",
        "        # a state in which the agent can perform a valid action\n",
        "        if rewards[s] not in (obstacleReward,goalReward):\n",
        "            # estimate action values for all possible actions from state s\n",
        "            Q = lookahead(s, actions, V, gamma, deterministic)\n",
        "            # greedily update the policy\n",
        "            aNew = np.where(Q==Q.max())[0]\n",
        "            for a in actions:\n",
        "                policy[s][a] = 1/len(aNew) if a in aNew else 0\n",
        "    return V, policy\n",
        "\n",
        "\n",
        "def plotPolicy(policy):\n",
        "    plt.rc('figure', figsize=(6,6))\n",
        "    ax = plt.gca()\n",
        "    ax.axis([0,gridSize[1],0,gridSize[0]])\n",
        "    ax.grid(True, color='k', linewidth=1.5)\n",
        "    ax.set_aspect(1)\n",
        "    ax.invert_yaxis()\n",
        "    ax.set_yticklabels([])\n",
        "    ax.yaxis.set_ticks_position('none')\n",
        "    ax.set_xticklabels([])\n",
        "    ax.xaxis.set_ticks_position('none')\n",
        "    for s in np.ndindex(gridSize):\n",
        "        if policy[s].max()==0:\n",
        "            if s in goal:\n",
        "                ax.add_patch(Rectangle((s[1],s[0]),1,1,color='springgreen'))\n",
        "            else:\n",
        "                ax.add_patch(Rectangle((s[1],s[0]),1,1,color='orangered'))\n",
        "        else:\n",
        "            if s in stars:\n",
        "                ax.add_patch(Rectangle((s[1],s[0]),1,1,color='royalblue'))\n",
        "            action = np.argmax(policy[s])\n",
        "            if action==0:\n",
        "                ax.arrow(s[1]+0.5,s[0]+0.8, 0,-0.6, head_width=0.25, head_length=0.15,\n",
        "                         linewidth=2, length_includes_head=True, fill=True)\n",
        "            elif action==1:\n",
        "                ax.arrow(s[1]+0.5,s[0]+0.2, 0,0.6, head_width=0.25, head_length=0.15,\n",
        "                         linewidth=2, length_includes_head=True, fill=True)\n",
        "            elif action==2:\n",
        "                ax.arrow(s[1]+0.2,s[0]+0.5, 0.6,0, head_width=0.25, head_length=0.15,\n",
        "                         linewidth=2, length_includes_head=True, fill=True)\n",
        "            elif action==3:\n",
        "                ax.arrow(s[1]+0.8,s[0]+0.5, -0.6,0, head_width=0.25, head_length=0.15,\n",
        "                         linewidth=2, length_includes_head=True, fill=True)\n",
        "            elif action==4:\n",
        "                ax.arrow(s[1]+0.25,s[0]+0.75, 0.5,-0.5, head_width=0.25, head_length=0.15,\n",
        "                         linewidth=2, length_includes_head=True, fill=True)\n",
        "            elif action==5:\n",
        "                ax.arrow(s[1]+0.75,s[0]+0.75, -0.5,-0.5, head_width=0.25, head_length=0.15,\n",
        "                         linewidth=2, length_includes_head=True, fill=True)\n",
        "            elif action==6:\n",
        "                ax.arrow(s[1]+0.25,s[0]+0.25, 0.5,0.5, head_width=0.25, head_length=0.15,\n",
        "                         linewidth=2, length_includes_head=True, fill=True)\n",
        "            elif action==7:\n",
        "                ax.arrow(s[1]+0.75,s[0]+0.25, -0.5,0.5, head_width=0.25, head_length=0.15,\n",
        "                         linewidth=2, length_includes_head=True, fill=True)\n",
        "    plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CSzKvvzD7o4h"
      },
      "source": [
        "# Task 3.1\n",
        "\n",
        "Compute the expected value of all cells for a policy that chooses with probability 0.5 a random action and otherwise moves towards the right."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CvbRcWIp4AkD",
        "outputId": "d5fb9234-636c-4b04-ab1f-0f85652effee",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 173
        }
      },
      "source": [
        "# only first four actions (Up, Down, Right, Left)\n",
        "actions = range(4)\n",
        "policy = initPolicy(actions)\n",
        "V = policyEvaluation(policy, actions)\n",
        "print(V)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ -55.75305866  -60.31658695  -76.24676467  -85.96864553  -95.1972291  -102.08834927 -109.17118645 -128.05561988 -154.37574107]\n",
            " [ -70.27159998  -71.06629982  -82.45365375  -97.07539187 -113.47895379    0.         -138.87299585    0.         -140.14102741]\n",
            " [-114.39151884    0.            0.            0.            0.            0.         -156.46207351    0.          -71.58727143]\n",
            " [-113.52630773    0.          -67.76537737  -82.31636096 -104.30515042 -131.6906198     0.           67.9743342     0.        ]\n",
            " [ -66.90692249  -61.73563943  -77.46923809    0.            0.            0.          -51.57546628  -41.73236875  -63.12418182]\n",
            " [ -64.50589789  -63.88385838  -69.5462395   -77.90234452  -83.20065591  -88.82932973  -95.52472879    0.         -145.97280746]\n",
            " [ -81.44265181    0.            0.            0.            0.            0.            0.         -146.7009558  -167.46397771]\n",
            " [ -24.10633623  -19.86287103  -28.53220248  -42.34223503  -57.42132599  -75.0898424  -100.98399693 -122.17565646    0.        ]\n",
            " [ -29.41531147  -33.26207267  -49.06898531  -73.95000655    0.          -85.58975449 -105.12793306 -125.22044776    0.        ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h6fEfLvG7sys"
      },
      "source": [
        "# Task 3.2\n",
        "\n",
        "Use the Policy Iteration algorithm to compute the optimal value V\\*(s) for each cell.\n",
        "\n",
        "Indicate the resulting optimal policy π\\*(s) with arrows in each cell."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aNWy0Vavot5V",
        "outputId": "d94060cc-1c8d-4338-a6f8-8fd0961291e1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 531
        }
      },
      "source": [
        "# only first four actions (Up, Down, Right, Left)\n",
        "actions = range(4)\n",
        "V, policy = policyIteration(actions)\n",
        "print(V,'\\n')\n",
        "plotPolicy(policy)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[100.         100.         100.         100.          89.          88.9998083   99.99982747  99.99984473  99.99986025]\n",
            " [100.         100.         100.          89.          79.1          0.          88.99984473   0.          99.99987423]\n",
            " [ 89.           0.           0.           0.           0.           0.          79.09986025   0.         100.        ]\n",
            " [ 79.1          0.         100.         100.         100.         100.           0.         100.           0.        ]\n",
            " [ 89.         100.         100.           0.           0.           0.          79.1         89.         100.        ]\n",
            " [ 79.1         89.         100.          89.          79.1         70.19        70.19         0.          89.        ]\n",
            " [ 89.           0.           0.           0.           0.           0.           0.          89.          79.1       ]\n",
            " [100.         100.         100.         100.         100.         100.         100.         100.           0.        ]\n",
            " [100.         100.         100.         100.           0.         100.         100.         100.           0.        ]] \n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b2X4MMUi7u_i"
      },
      "source": [
        "# Task 3.3\n",
        "\n",
        "Extend the action set by also allowing diagonal moves, such that the agent can move to its eight neighboring cells.\n",
        "\n",
        "Use the Value Iteration algorithm to compute the optimal value V\\*(s) for each cell.\n",
        "\n",
        "Indicate the resulting optimal policy π\\*(s) with arrows in each cell.\n",
        "\n",
        "Discuss how value and policy changed, compared to Task 3.2."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CKREvWLhqZya",
        "outputId": "4d74175b-9b8c-4387-9786-efce14ca1fa4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 531
        }
      },
      "source": [
        "# all eight actions (diagonal moves allowed as well)\n",
        "actions = range(8)\n",
        "V, policy = valueIteration(actions)\n",
        "print(V,'\\n')\n",
        "plotPolicy(policy)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 99.99957435  99.99961692  99.99965523  99.9996897   88.99972073  88.99999977  99.99999975  99.9999998   99.99999982]\n",
            " [ 99.99965523  99.9996897   99.9996897   99.9996897   88.99972073   0.          99.99999982   0.          99.99999984]\n",
            " [ 88.99972073   0.           0.           0.           0.           0.          99.99999952   0.         100.        ]\n",
            " [ 88.99999941   0.          99.99999947  99.99999952  99.99999957  99.99999961   0.         100.           0.        ]\n",
            " [ 88.99999952  99.99999952  99.99999957   0.           0.           0.          99.99999965 100.         100.        ]\n",
            " [ 89.          99.99999961  99.99999961  99.99999961  88.99999965  88.99999969  89.           0.          89.        ]\n",
            " [100.           0.           0.           0.           0.           0.           0.         100.          89.        ]\n",
            " [100.         100.         100.         100.         100.         100.         100.         100.           0.        ]\n",
            " [100.         100.         100.         100.           0.         100.         100.         100.           0.        ]] \n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ITVKyp3R4pdN"
      },
      "source": [
        "### Optimal Policy Comparison (Task 3.2 vs 3.3)\n",
        "\n",
        "1. With the introduction of more moves, it becomes possible to reach G (or higher reward states) more easily (fewer steps) than before from any particular state which leads to higher state value. Therefore, we see in few places, the optimal value has increased as compared to Task 3.2\n",
        "\n",
        "2. One other way to see it is to see the value of the state around G. It is possible to reach G from 5 states out of which one marked 'x' is not considered. Of the remaining 4 states, it was possible to reach G using non-diagnol move from 3 states and using diagnol move from one state. In Task 3.2, those 3 states have value 100 and the diagnol one - 89 (because can't reach G in one move) whereas for Task 3.3 all 4 states have value 100 because G can be reached in one step for this case."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3ERNnY6Q7xOz"
      },
      "source": [
        "# Task 3.4\n",
        "\n",
        "Consider non-deterministic actions, where the agent moves with probability 0.8 into the desired direction, but with probability 0.1 deviates 45° to the left and with probability 0.1 deviates 45° to the right of the desired direction.\n",
        "\n",
        "Compute again V\\*(s) and indicate π\\*(s) with arrows.\n",
        "\n",
        "Discuss how value and policy changed, compared to Task 3.3."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4TpoQdqQqasH",
        "outputId": "a92a1f3c-6f4f-438d-b541-bec4268ef6fc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 531
        }
      },
      "source": [
        "# all eight actions for non-deterministic\n",
        "actions = range(8)\n",
        "V, policy = valueIteration(actions, deterministic=False)\n",
        "print(V,'\\n')\n",
        "plotPolicy(policy)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[77.97918981 76.38986152 74.58877395 72.98560843 67.03602177 77.81690424 87.57442039 89.74419816 88.37785042]\n",
            " [80.03823129 80.03823129 78.58877749 75.88561166 67.0360502   0.         87.57449834  0.         90.64680704]\n",
            " [71.03440816  0.          0.          0.          0.          0.         88.11416367  0.         98.7653956 ]\n",
            " [83.75461674  0.         94.63885605 95.68550278 92.8629175  90.35050665  0.         98.5043956   0.        ]\n",
            " [84.63296084 95.23169626 95.26916865  0.          0.          0.         88.11418512 98.5043956  95.6043956 ]\n",
            " [84.63298197 94.39233461 92.49233461 92.49233461 79.14152649 77.97685307 84.49292356  0.         87.39295604]\n",
            " [98.89999998  0.          0.          0.          0.          0.          0.         96.70329668 88.70329668]\n",
            " [99.99999998 99.99999998 99.99999998 99.99999998 99.99999998 99.99999998 99.99999998 99.99999998  0.        ]\n",
            " [99.99999998 99.99999999 99.99999999 99.99999999  0.         99.99999999 99.99999999 99.99999999  0.        ]] \n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UrBmefdc8LUL"
      },
      "source": [
        "### Optimal Policy Comparison (Task 3.3 vs 3.4)\n",
        "\n",
        "1. At the edges, in Task 3.3 since there was no probability of deviation from action the policy allows movement along the edge if the action value is greater in that direction, though in Task 3.4 it can be since most of those direction point away from the edge - so that even if there is deviation it still doesn't collide with the wall and get a negative reward. Similar is the case for the 'X' where it may also get a negative reward.\n",
        "\n",
        "2. Interestingly, the action values for both the task is similar despite policy being different as discussed in $1$ : which suggests that for each state there is more than one optimal action(or optimal policy)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mOYG7FrYk2AY"
      },
      "source": [
        "### Without Local Rewards\n",
        "Overall we see places far away from G getting high state value as well - this is because of the presence of local points (+10) and therefore the policy keeps oscillating there. Methods can be further verified by eliminating these local rewards and we should see state values decrease as we move further from 'G'."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4arGjT2RmYiO",
        "outputId": "af79c37e-5ae0-4238-e665-b3b93e463052",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 531
        }
      },
      "source": [
        "# removing local rewards\n",
        "rewards[np.where(rewards==10)] = 0\n",
        "# all eight actions\n",
        "actions = range(8)\n",
        "V, policy = valueIteration(actions)\n",
        "print(V,'\\n')\n",
        "\n",
        "plt.rc('figure', figsize=(6,6))\n",
        "ax = plt.gca()\n",
        "ax.axis([0,gridSize[1],0,gridSize[0]])\n",
        "ax.grid(True, color='k', linewidth=1.5)\n",
        "ax.set_aspect(1)\n",
        "ax.invert_yaxis()\n",
        "ax.set_yticklabels([])\n",
        "ax.yaxis.set_ticks_position('none')\n",
        "ax.set_xticklabels([])\n",
        "ax.xaxis.set_ticks_position('none')\n",
        "for s in np.ndindex(gridSize):\n",
        "    # if no action possible in state s i.e. obstacle or goal state\n",
        "    if policy[s].max()==0:\n",
        "        # if goal state\n",
        "        if s in goal:\n",
        "            ax.add_patch(Rectangle((s[1],s[0]),1,1,color='springgreen'))\n",
        "        # if obstacle\n",
        "        else:\n",
        "            ax.add_patch(Rectangle((s[1],s[0]),1,1,color='orangered'))\n",
        "    else:\n",
        "        action = np.argmax(policy[s])\n",
        "        if action==0:\n",
        "            ax.arrow(s[1]+0.5,s[0]+0.8, 0,-0.6, head_width=0.25, head_length=0.15,\n",
        "                     linewidth=2, length_includes_head=True, fill=True)\n",
        "        elif action==1:\n",
        "            ax.arrow(s[1]+0.5,s[0]+0.2, 0,0.6, head_width=0.25, head_length=0.15,\n",
        "                     linewidth=2, length_includes_head=True, fill=True)\n",
        "        elif action==2:\n",
        "            ax.arrow(s[1]+0.2,s[0]+0.5, 0.6,0, head_width=0.25, head_length=0.15,\n",
        "                     linewidth=2, length_includes_head=True, fill=True)\n",
        "        elif action==3:\n",
        "            ax.arrow(s[1]+0.8,s[0]+0.5, -0.6,0, head_width=0.25, head_length=0.15,\n",
        "                     linewidth=2, length_includes_head=True, fill=True)\n",
        "        elif action==4:\n",
        "            ax.arrow(s[1]+0.25,s[0]+0.75, 0.5,-0.5, head_width=0.25, head_length=0.15,\n",
        "                     linewidth=2, length_includes_head=True, fill=True)\n",
        "        elif action==5:\n",
        "            ax.arrow(s[1]+0.75,s[0]+0.75, -0.5,-0.5, head_width=0.25, head_length=0.15,\n",
        "                     linewidth=2, length_includes_head=True, fill=True)\n",
        "        elif action==6:\n",
        "            ax.arrow(s[1]+0.25,s[0]+0.25, 0.5,0.5, head_width=0.25, head_length=0.15,\n",
        "                     linewidth=2, length_includes_head=True, fill=True)\n",
        "        elif action==7:\n",
        "            ax.arrow(s[1]+0.75,s[0]+0.25, -0.5,0.5, head_width=0.25, head_length=0.15,\n",
        "                     linewidth=2, length_includes_head=True, fill=True)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 39.2513931   43.612659    48.45851     54.9539      62.171       70.19        72.09        80.1         80.1       ]\n",
            " [ 39.2513931   43.612659    48.45851     54.9539      62.171        0.          79.1          0.          89.        ]\n",
            " [ 40.1369831    0.           0.           0.           0.           0.          89.           0.         100.        ]\n",
            " [ 45.707759     0.          57.6639      64.071       71.19        79.1          0.         100.           0.        ]\n",
            " [ 45.707759    51.89751     57.6639       0.           0.           0.          89.         100.         100.        ]\n",
            " [ 45.707759    51.89751     54.9539      62.171       70.19        79.1         89.           0.          89.        ]\n",
            " [ 45.707759     0.           0.           0.           0.           0.           0.          79.1         79.1       ]\n",
            " [ 40.1369831   41.4464931   46.051659    51.16851     56.8539      63.171       70.19        70.19         0.        ]\n",
            " [ 37.30184379  41.4464931   46.051659    51.16851      0.          63.171       63.171       63.171        0.        ]] \n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}